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A081611
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Number of numbers <= n having no 2 in their ternary representation.
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6
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1, 2, 2, 3, 4, 4, 4, 4, 4, 5, 6, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 10, 11, 12, 12, 12, 12, 12, 13, 14, 14, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16
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OFFSET
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0,2
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COMMENTS
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a(n) + A081610(n) = n+1.
a(n) is also the size of the subset of [1...n] when numbers are added greedily so as to not contain a 3-term arithmetic progression, i.e., according to A003278: a(n) = the largest k such that A003278(k) <= n. (Cf. A003002, the size of the optimal (largest) 3-free subset of [1...n]) [From R. Shreevatsa (shreevatsa.public(AT)gmail.com), Oct 19 2009]
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 0..10000
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FORMULA
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G.f. A(x) satisfies A(x)=(1+x)(1+x+x^2)A(x^3). - Michael Somos Aug 31 2006
G.f.: (1/(1-x))Product{k>=0} 1+x^(3^k). - Michael Somos Aug 31 2006
a(n)=a(n-1)+A039966(n). - Michael Somos Aug 31 2006
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PROG
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(PARI) {a(n)=local(A, m); if(n<0, 0, m=1; A=1+O(x); while(m<=n, m*=3; A=(1+x)*(1+x+x^2)*subst(A, x, x^3)); polcoeff(A, n))} /* Michael Somos Aug 31 2006 */
(Haskell)
a081611 n = a081611_list !! n
a081611_list = scanl1 (+) a039966_list
-- Reinhard Zumkeller, Jan 28 2012
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CROSSREFS
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Cf. A007089, A081603, A081608, A061392.
Number of terms in A003278 that are <=n. [From R. Shreevatsa (shreevatsa.public(AT)gmail.com), Oct 19 2009]
Sequence in context: A095395 A029134 A029130 * A081228 A003002 A087180
Adjacent sequences: A081608 A081609 A081610 * A081612 A081613 A081614
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, Mar 23 2003
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STATUS
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approved
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